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Semiparametric model-based inference in the presence of missing responses

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  • Qihua Wang
  • Pengjie Dai

Abstract

We consider a semiparametric model that parameterizes the conditional density of the response, given covariates, but allows the marginal distribution of the covariates to be completely arbitrary. Responses may be missing. A likelihood-based imputation estimator and a semi-empirical-likelihood-based estimator for the parameter vector describing the conditional density are defined and proved to be asymptotically normal. Semi-empirical loglikelihood functions for the parameter vector and the response mean are derived. It is shown that the two semi-empirical loglikelihood functions are distributed asymptotically as weighted χ-super-2 and scaled χ-super-2, respectively. Copyright 2008, Oxford University Press.

Suggested Citation

  • Qihua Wang & Pengjie Dai, 2008. "Semiparametric model-based inference in the presence of missing responses," Biometrika, Biometrika Trust, vol. 95(3), pages 721-734.
    • Handle: RePEc:oup:biomet:v:95:y:2008:i:3:p:721-734
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    File URL: http://hdl.handle.net/10.1093/biomet/asn032
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    Cited by:

    1. Liu, Tianqing & Yuan, Xiaohui, 2012. "Combining quasi and empirical likelihoods in generalized linear models with missing responses," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 39-58.
    2. Zhong Guan & Jing Qin, 2017. "Empirical likelihood method for non-ignorable missing data problems," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 23(1), pages 113-135, January.
    3. Zhou, Jing & Lan, Wei & Wang, Hansheng, 2022. "Asymptotic covariance estimation by Gaussian random perturbation," Computational Statistics & Data Analysis, Elsevier, vol. 171(C).
    4. Biao Zhang, 2016. "Empirical Likelihood in Causal Inference," Econometric Reviews, Taylor & Francis Journals, vol. 35(2), pages 201-231, February.
    5. Xie Yanmei & Zhang Biao, 2017. "Empirical Likelihood in Nonignorable Covariate-Missing Data Problems," The International Journal of Biostatistics, De Gruyter, vol. 13(1), pages 1-20, May.

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